Reader Question – How Did Mariners Navigate by the Stars?

Way back last December, we received a question from David Spangler in PA who writes:

Dear Jay, You asked for astronomy questions: mine is a simple one, I think. I’ve always wondered how mariners have used stars to navigate. Is it as simple as locating star alignments known to point in a certain general direction (e.g. north)? If so, aren’t there significant limitations of precision in this method, especially when applied to navigating even a moderately long distance?

We also received this from Tyler Hogan from Bright Ideas Press who remarked:

I noticed you mentioned in the introduction that you were considering doing books on navigation, geometry, and/or physics via astronomy. Are they in the works? I’ve read so many books on ancient astronomers and navigators, but never any that explained how they did their calculations or how to reproduce them yourself.

I love questions like these! David’s question explains the part that he does actually understand, and indicates the specific points where his understanding is incomplete. Tyler points out that many writers allude to celestial navigational methods, but never delve into specifics.

In order to discuss celestial navigation, we have to understand that simple geometry is required in order to measure angles in the sky. As mentioned in detail in Chapter 2 of Signs & Seasons , the starry sky gives the illusion of being an enormous “celestial sphere.” Though this is understood to be an illusion, we can nevertheless employ this illusion to draw circles on the celestial sphere, such as the horizon, equator, meridian, and ecliptic, as also explained throughout Signs & Seasons.

If we can define circles on the celestial sphere, we can also define “pie slice” segments of such circles. Since a circle, in geometry, is measured as 360 degrees, we can measure smaller segments, representing angles of 90 degrees, 30 degrees, or any such angles as we might imagine. In this way, we can measure the angular “distance” between two stars, or between any other two objects including the Sun, Moon, or planets, as being placed at two points on a “pie slice” segment of a circle. In this way, we can precisely measure positions of celestial objects at specific times, for example, “the Moon is seven degrees from Jupiter on September 23.”

Upcoming Signs & Seasons Sequels from Fourth Day Press

As Tyler inquired. there is a sequel to Signs & Seasons in the works which will discuss how angle measurement and Classical Geometry have historically been used in Classical Astronomy to measure the positions and motions of the Sun, Moon, stars and planets. This second book in the series will be directed at highschoolers, and will be intended to count as a math elective. This book is in production, but progress has not proceeded quickly due to commitments with family and my day job. We’d be grateful for everyone’s prayers, that the LORD would graciously enable me to make the time to work on that.

A third book in the series is planned that will discuss Classical Geography as it pertains to Classical Astronomy. These are the aspects of how our view of the sky varies with position on the Earth:

  • why the seasons are reversed in the opposite hemisphere;
  • why the period of daylight is so long or short in the polar regions;
  • why the days are always 12 hours long on the Equator; and
  • why the Tropics are named for Cancer and Capricorn, etc.

As with other aspects of Classical Astronomy, these are things of which most people have heard, but are very poorly understood. In fact, it is these very aspects which enabled the navigators of old to sail the world, and find their way to their destinations and back home again, using simple geometrical instruments. The ancient navigation methods are actually quite simple to understand if one has a basic visual understanding of the sky. The entire Signs & Seasons course is intended to lay a foundation upon which an understanding of such things can be built.

We will touch on some of these points in this article, and look forward to a future time when we can prepare the curriculum.

Finding Direction from the Sky

As David mentioned in his question, sky watchers in the northern hemisphere can find north by following the stars of the Big Dipper to Polaris, the North Star, as discussed on page 46 of Signs & Seasons. This is a remarkable arrangement of stars, which I consider evidence of the LORD’s providence, in designing such a useful, conspicuous arrangment of stars by which men could navigate around the Earth’s surface.

In this way, the northern constellations have been used by European navigators to find north for all of history. This technique of navigating by the Big Dipper (or, the Great Bear) is mentioned in Homer’s Odyssey, (circa 700 B.C.) one of the oldest works of western literature:

She made the wind fair and warm for him, and gladly did Ulysses spread his sail before it, while he sat and guided the raft skilfully by means of the rudder. He never closed his eyes, but kept them fixed on the Pleiads, on late-setting Bootes, and on the Bear — which men also call the wain, and which turns round and round where it is, facing Orion, and alone never dipping into the stream of Oceanus.

The Big Dipper and Polaris are still useful in modern times for finding direction. In a famous example, African-American slaves in antebellum times would “follow the drinking gourd” to find freedom in the north. I myself have routinely used the Big Dipper to find direction, particularly when traveling in unfamiliar areas.

Besides simply finding north with the Big Dipper, a general familiarity of the constellations enables one to locate all the compass points at night. As also explained in Chapter 2 of Signs & Seasons , all the constellations reach their highest point in the sky when reaching the meridian. At other times, the constellations are either rising or setting, and are thus lower in the sky. By simply locating the constellations at the meridian, and also identifying the constellations rising and setting, the entire sky can present a type of navigational map for which each point of the compass can be easily located, north, east, west and south. The navigators of old could find any direction of a 32 point “compass rose” simply by making an experienced observation of the positions of the stars in the night sky.

Latitude Sailing

Most people are familiar with the fact that latitude and longitude are used as coordinates for locating positions on the Earth. However, most people are not aware that these coordinates are directly drawn from astronomy, and correspond with similar coordinates in the sky.

For example, Signs & Seasons explains that there are celestial poles in the night sky, similar to the terrestrial poles on the Earth. Similarly, the sky has a celestial equator that directly corresponds to the Equator on the Earth. The celestial poles and equator are part of a coordinate system of the sky that is based on declination and right ascension, where declination corresponds with latitude, and right ascension more or less corresponds with longitude.

Just like the terrestrial Equator is zero latitude, the celestial equator is zero declination. And as the North Pole on Earth is at a latitude of 90 degrees north, the celestial north pole is at a declination of 90 degrees north. For any given latitude on the Earth, the stars at the corresponding declination are directly overhead, passing through the zenith of that location.

For example, if one were on the Equator, such as in the countries of Equador, Zaire, or Indonesia, the stars of the celestial equator pass directly overhead at the zenith. Since the stars of Orion’s belt are right on the celestial equator, these stars pass directly overhead as seen from Equador.

Similarly, if one were standing at the North Pole on Earth, the North Star Polaris would be directly overhead at the zenith. For all other latitudes, the stars at the corresponding declinations pass through the zenith. Most large American cities are near latitude 40 degrees north. Therefore, the stars Deneb and Vega, pass near the zenith. These stars are part of the Summer Triangle, and are visible in the evening sky from about August through October.

If a navigator is familiar with the constellations, and has a star map or globe that indicates declination, one can determine latitude simply from finding the stars near the zenith. As a ship sails into high northern latitudes, the Big Dipper is increasingly high overhead. This is why the Big Dipper is featured on the state flag of Alaska, since these stars are very prominent in the night sky.

Similarly, as a ship sails into the southern hemisphere, the stars of the southern sky appear higher and more prominent in the night sky. This is why the Southern Cross is featured prominently on the flags of Australia and New Zealand.

The shifting of the positions of the stars overhead is undeniable proof that the Earth is round. This would not happen if the Earth were flat. This fact was well known in ancient times, and is included in the historical proofs of the Earth’s sphericity given by Aristotle (circa 330 B.C.) Contrary to popular belief, the sphericity of the Earth was well known in the Middle Ages and also time of Columbus, and this was proved and understood for centuries prior to his historic voyages.

Another very simple, traditional method of finding latitude is to measure the angular elevation of the North Star above the horizon. To illustrate, at the Equator, the celestial equator is at the zenith. Therefore, the North Star sits directly on the horizon, since it is 90 degrees from the zenith. The Equator is zero latitude. As one moves to latitudes north of the Equator, the North Star becomes visible above the horizon.

For example, at 10 degrees latitude north, the North Star is 10 degrees above the horizon. At latitude 20 degrees north, the North Star is 20 degrees above the horizon, and so on. At latitude 90 degrees north, the North Pole, the North Star is 90 degrees above the horizon, or at the zenith, as we have already seen. For observers in American cities near latitude 40 degrees north, Polaris is seen at an angular elevation of 40 degrees above the horizon, nearly at the midpoint between the horizon and the zenith.

To measure the elevation of the Polaris, the old navigators used a quadrant, which was simply a quarter circle having a scale with angle markings from zero to 90 degrees, and also a plumb bob to mark the angle to which the instrument is slanted. The navigator would slant the quadrant and sight his eye along the slanted edge, and read the place where the plumb bob crossed the scale to learn the elevation of Polaris, and hence the latitude. The modern sextant is simply a more mechanically-sophisticated instrument based on the same principle, for finding angular elevations of celestial bodies above the horizon.

Using this technique and other similar techniques, the old navigators would sail along the latitudes, to the New World and beyond, without the benefit of radar, GPS, or any other modern electronic conveniences. Yet these simple techniques are still valid, and still useful to modern navigators in the event of a power failure.

The Quest for Longitude

Columbus made his voyages using latitude sailing, as did the Spanish conquistadors. However, the problem with latitude sailing is that you need to also know longitude in order to avoid sand bars and islands and other obstacles at sea. Many a Spanish galleon, loaded with the Aztec gold of Mexico, was run aground as a result of poor longitude estimates. While this might be a good thing for modern salvage operations, it was a bad thing for the interests of the 16th century Spanish kings.

A detailed discussion of the quest for longitude is given in the popular book Longitude by Dava Sobel. To make a long story short, the ultimate solution was discovered in the 1700s by Englishman John Harrison, who invented the chronometer, a clock that kept very precise time at sea. The general principle was that the chronometer would enable a ship at sea to discover its place within a “time zone.”

The chronometer would maintain the exact time of the Royal Greenwich Observatory. A special “Nautical Almanack” was published at Greenwich to include specific celestial events such as eclipses and lunar conjunctions, and recorded the precise times of these events as they would be observed at Greenwich. A navigator would compare the local times of these events, as seen at sea, and subtract to find the time difference between the ship’s location and Greenwich.

Each difference of four minutes corresponded to one degree of longitude. For example, a navigator in the Atlantic might observe a conjunction of the Moon with Jupiter, and note a time difference of 4 hours, 40 minutes compared to the time recorded in the Nautical Almanack. This would indicate that the ship was at longitude 70 degrees, and approaching the east coast of the United States.

Each 15 degrees of longitude corresponds to a full hour of time difference, which is the basis for our system of standard time zones used in our modern world today. The British Nautical Almanack was so useful that sailors all over the world used it to set their chronometers. In this way, the Greenwich Meridian was defined as the Prime Meridian, “longitude zero” for the world’s system of standard time.

For example, Philadelphia, Pennsylvania is at 75 degrees longitude west of Greenwich. Therefore, the eastern standard time zone (EST) is five hours behind Greenwich Mean Time (GMT). Each of the 24 time zones in the world are defined by 15 degree increments of longitude, to the east or west of Greenwich.

Circles of Position

It was inefficient to make separate measurements for both longitude and latitude. Each measurement included errors, and the combination of these two measurements resulted in imprecision in finding port. After centuries of navigation at sea, the circle of position technique was finally developed in the 1830s that incorporated both latitude and longitude.

The concept of circles of position can be difficult to grasp, and requires a fairly deep understanding of visual astronomy in order to form a clear mental picture. Imagine that the elevation of Polaris is the same at each point along the same circle of latitude. For example, all observers at latitude 40 degrees north will see Polaris 40 degrees above the horizon. This latitude would be one circle of position.

Similarly, for any given star in any part of the sky, at any given elevation, there would be a circle on the Earth’s surface where the star would be visible at that elevation. For example, suppose a sailor observes the star Sirius at 20 degrees above the horizon. There would be a circle on the Earth’s surface, cutting across many longitudes and latitudes, where Sirius would be at an elevation of 20 degrees.

If you measure the elevation of a number of stars at your location at sea, you’d find a place on the globe where all these circles would cross. That ends up being your exact position on the Earth. By finding the time on your chronometer, you can locate your longitude, and the latitude would follow from the same measurement.

Great precision of measurement can be found using spherical trigonometry. There are mathematical techniques for measuring angles along the curved surface of a sphere, just as the more familiar plane trigonometry can be used to measure angles on flat surfaces. Since the starry sky appears to be a sphere, spherical trigonometry can be used to precisely calculate position at sea from the positions of stars. Lots of mathematical calculations are involved, but a multi-volume set of spherical triangle tables were published to make the procedure simple for the common seaman.

By using a sextant to precisely measure the Sun, Moon, star or planet at any given time, based on the chronometer, a navigator could pinpoint the ship’s position at sea to within a nautical mile (which corresponds to one arcminute of latitude, somewhat larger than a regular statute mile).

The techniques of celestial navigation are all but forgotten today, having been displaced by electronic methods employing radar and the satellite array of the Global Positioning System (GPS), which can be accurate to a fraction of an arcsecond of latitude. However, if the lights were to ever go out on a ship, the wise navigator would do well to learn the stars and keep a sextant handy, lest his ship be lost at sea.

Jay Ryan is the author of Signs & Seasons, an illustrated, Biblically-centered homeschool curriculum for Classical Astronomy. He is also the creator of the Classical Astronomy Update, an email astronomy newseltter especially for Christian homeschoolers.  Visit his website at

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